A strong failure of ℵ -stability for atomic classes

Michael C. Laskowski; Saharon Shelah

doi:10.1007/s00153-018-0623-6

A strong failure of ℵ -stability for atomic classes

Michael C. Laskowski^*, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study classes of atomic models At_T of a countable, complete first-order theory T. We prove that if At_T is not pcl -small, i.e., there is an atomic model N that realizes uncountably many types over pcl _N(a¯) for some finite a¯ from N, then there are 2ℵ1 non-isomorphic atomic models of T, each of size ℵ₁.

Original language	English
Pages (from-to)	99-118
Number of pages	20
Journal	Archive for Mathematical Logic
Volume	58
Issue number	1-2
DOIs	https://doi.org/10.1007/s00153-018-0623-6
State	Published - 5 Feb 2019

Bibliographical note

Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

Keywords

Atomic models
Non-structure
Pseudo-algebraic

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10.1007/s00153-018-0623-6

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A strong failure of ℵ -stability for atomic classes

Abstract

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Keywords

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